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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Growth rates for monotone subsequences


Authors: A. del Junco and J. Michael Steele
Journal: Proc. Amer. Math. Soc. 71 (1978), 179-182
MSC: Primary 10K05
DOI: https://doi.org/10.1090/S0002-9939-1978-0491571-6
MathSciNet review: 0491571
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Abstract: The growth rate of the largest monotone subsequence of a uniformly distributed sequence is obtained. For ${a_n} = n\alpha \bmod \; 1$ with $\alpha$ algebraic irrational the exponent of growth is found to be precisely the same as for a random sequence.


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Keywords: Monotone subsequence, uniform distribution, algebraic irrationals, discrepancy
Article copyright: © Copyright 1978 American Mathematical Society